Heat capacity and compactness of denatured proteins

Two-dimensional (P/T) studies of secondary/tertiary conformational dynamics in nucleic acids: pressure induced melting and Maxwell relations at the single molecule level

A predictive understanding of conformational folding of nucleic acids depends crucially on the underlying competition between enthalpic and entropic contributions to overall free energy changes. In extreme environments (e.g. deep ocean vents), such free energy changes are in turn impacted by both pressure and temperature as strongly coupled intensive variables, emphasizing the importance of a detailed molecular level understanding of the underlying thermodynamics. In this work, single-molecule fluorescence energy resonance transfer (smFRET) microscopy methods are implemented for quantitative kinetic study of secondary structure (i.e., DNA hybridization) and tertiary structure (i.e., RNA Mn2+ riboswitch folding) equilibria as a function of both pressure (P = 1 to 1000 bar) and temperature (T = 21 to 27 °C). Temperature dependent studies at a series of fixed pressures reveal the single molecule DNA and RNA constructs to be stabilized and destabilized, respectively, with increasing T. Interestingly, results for the Mn2+ riboswitch indicate a positive entropy change (ΔS > 0) for achieving the native tertiary conformation at all external pressures. This is contrary to more common physical expectations of increased order and thus an entropically penalty for tertiary folding of the RNA. On the other hand, pressure dependent scans for a series of constant temperature conditions confirm that both the DNA hairpin and RNA riboswitch constructs destabilize ("melt") under increasing pressure, which by van't Hoff analysis implies a positive volume change (ΔV0 > 0) for both secondary and tertiary folding into the native state. Furthermore, slices through these two-dimensional free energy surfaces permit parameters for isobaric thermal expansion in both secondary and tertiary conformational folding coordinates to be extracted. Finally, experimental control of multiple variables allows determination of the folding free energies as a two-dimensional function of pressure and temperature (ΔG(P, T)). To the best of our knowledge, this facilitates a first experimental confirmation of the underlying Maxwell relation (∂ΔS/∂P)T = -(∂ΔV/∂T)P for the exact free energy differential dG(P, V, S, T) at the single molecule level.

Why small proteins tend to have high denaturation temperatures

Data indicate that small globular proteins (consisting of less than about 70 residues) tend to have high denaturation temperatures. This finding is analysed by comparing experimental denaturation enthalpy and entropy changes of a selected set of small proteins with values calculated on the basis of average and common properties of globular proteins. The conclusion is that the denaturation entropy change is smaller than expected, leading to an increase in denaturation temperature. The proposed molecular rationalization considers the existence of long-wavelength, low-frequency vibrational modes in the native state of small proteins due to their large surface-to-interior ratio. The effect of decreasing the conformational entropy gain associated with denaturation on thermal stability is directly verified by means of an already devised theoretical model [G. Graziano, Phys. Chem. Chem. Phys. 2010, 12, 14245-14252; 2014, 16, 21755-21767].

Comparative thermal unfolding study of psychrophilic and mesophilic subtilisin-like serine proteases by molecular dynamics simulations

Molecular dynamics (MD) simulations of a subtilisin-like serine protease VPR from the psychrophilic marine bacterium Vibrio sp. PA-44 and its mesophilic homologue, proteinase K (PRK), have been performed for 20 ns at four different temperatures (300, 373, 473, and 573 K). The comparative analyses of MD trajectories reveal that at almost all temperatures, VPR exhibits greater structural fluctuations/deviations, more unstable regular secondary structural elements, and higher global flexibility than PRK. Although these two proteases follow similar unfolding pathways at high temperatures, VPR initiates unfolding at a lower temperature and unfolds faster at the same high temperatures than PRK. These observations collectively indicate that VPR is less stable and more heat-labile than PRK. Analyses of the structural/geometrical properties reveal that, when compared to PRK, VPR has larger radius of gyration (Rg), less intramolecular contacts and hydrogen bonds (HBs), more protein-solvent HBs, and smaller burial of nonpolar area and larger exposure of polar area. These suggest that the increased flexibility of VPR would be most likely caused by its reduced intramolecular interactions and more favourable protein-solvent interactions arising from the larger exposure of the polar area, whereas the enhanced stability of PRK could be ascribed to its increased intramolecular interactions arising from the better optimized hydrophobicity. The factors responsible for the significant differences in local flexibility between these two proteases were also analyzed and ascertained. This study provides insights into molecular basis of thermostability of homologous serine proteases adapted to different temperatures.

The cytotoxicity of BAMLET complexes is due to oleic acid and independent of the α-lactalbumin component

•

We synthesized three different BAMLET complexes consisting of oleic acid coupled to bovine α-lactalbumin.

•

Oleic acid micelles alone are tumoricidal at equimolar concentrations of oleic acid bound in the BAMLET complexes.

•

α-Lactalbumin is non-toxic to cells even when delivered to their cytoplasm.

•

Both, BAMLET and oleic acid micelles showed no selective cytotoxicity to cancer cells.

Lipid–protein complexes comprised of oleic acid (OA) non-covalently coupled to human/bovine α-lactalbumin, named HAMLET/BAMLET, display cytotoxic properties against cancer cells. However, there is still a substantial debate about the role of the protein in these complexes. To shed light into this, we obtained three different BAMLET complexes using varying synthesis conditions. Our data suggest that to form active BAMLET particles, OA has to reach critical micelle concentration with an approximate diameter of 250 nm. Proteolysis experiments on BAMLET show that OA protects the protein and is probably located on the surface, consistent with a micelle-like structure. Native or unfolded α-lactalbumin without OA lacked any tumoricidal activity. In contrast, OA alone killed cancer cells with the same efficiency at equimolar concentrations as its formulation as BAMLET. Our data show unequivocally that the cytotoxicity of the BAMLET complex is exclusively due to OA and that OA alone, when formulated as a micelle, is as toxic as the BAMLET complex. The contradictory literature results on the cytotoxicity of BAMLET might be explained by our finding that it was imperative to sonicate the samples to obtain toxic OA.

On the mechanism of cold denaturation

A theoretical rationalization of the occurrence of cold denaturation for globular proteins was devised, assuming that the effective size of water molecules depends upon temperature [G. Graziano, Phys. Chem. Chem. Phys., 2010, 12, 14245-14252]. In the present work, it is shown that the latter assumption is not necessary. By performing the same type of calculations in water, 40% (by weight) methanol, methanol, and carbon tetrachloride, it emerges that cold denaturation occurs only in water due to the special temperature dependence of its density and the small size of its molecules. These two coupled factors determine the magnitude and the temperature dependence of the stabilizing term that measures the gain in configurational/translational entropy of water molecules upon folding of the protein. This term has to be contrasted with the destabilizing contribution measuring the loss in conformational entropy of the polypeptide chain upon folding.

Differential temperature-dependent multimeric assemblies of replication and repair polymerases on DNA increase processivity

Differentiation of binding accurate DNA replication polymerases over error prone DNA lesion bypass polymerases is essential for the proper maintenance of the genome. The hyperthermophilic archaeal organism Sulfolobus solfataricus (Sso) contains both a B-family replication (Dpo1) and a Y-family repair (Dpo4) polymerase and serves as a model system for understanding molecular mechanisms and assemblies for DNA replication and repair protein complexes. Protein cross-linking, isothermal titration calorimetry, and analytical ultracentrifugation have confirmed a previously unrecognized dimeric Dpo4 complex bound to DNA. Binding discrimination between these polymerases on model DNA templates is complicated by the fact that multiple oligomeric species are influenced by concentration and temperature. Temperature-dependent fluorescence anisotropy equilibrium binding experiments were used to separate discrete binding events for the formation of trimeric Dpo1 and dimeric Dpo4 complexes on DNA. The associated equilibria are found to be temperature-dependent, generally leading to improved binding at higher temperatures for both polymerases. At high temperatures, DNA binding of Dpo1 monomer is favored over binding of Dpo4 monomer, but binding of Dpo1 trimer is even more strongly favored over binding of Dpo4 dimer, thus providing thermodynamic selection. Greater processivities of nucleotide incorporation for trimeric Dpo1 and dimeric Dpo4 are also observed at higher temperatures, providing biochemical validation for the influence of tightly bound oligomeric polymerases. These results separate, quantify, and confirm individual and sequential processes leading to the formation of oligomeric Dpo1 and Dpo4 assemblies on DNA and provide for a concentration- and temperature-dependent discrimination of binding undamaged DNA templates at physiological temperatures.

Fluctuation theory of molecular association and conformational equilibria

General expressions relating the effects of pressure, temperature, and composition on solute association and conformational equilibria using the fluctuation theory of solutions are provided. The expressions are exact and can be used to interpret experimental or computer simulation data for any multicomponent mixture involving molecules of any size and character at any composition. The relationships involve particle-particle, particle-energy, and energy-energy correlations within local regions in the vicinity of each species involved in the equilibrium. In particular, it is demonstrated that the results can be used to study peptide and protein association or aggregation, protein denaturation, and protein-ligand binding. Exactly how the relevant fluctuating properties may be obtained from experimental or computer simulation data are also outlined. It is shown that the enthalpy, heat capacity, and compressibility differences associated with the equilibrium process can, in principle, be obtained from a single simulation. Fluctuation based expressions for partial molar heat capacities, thermal expansions, and isothermal compressibilities are also provided.

CHARMM: the biomolecular simulation program

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

Structural and thermodynamic studies of Bergerac-SH3 chimeras

Bergerac-type chimeras of spectrin SH3 were designed by extending a beta-hairpin by eight amino acids so that the extension protruded from the domain body like a "nose" being exposed to the solvent. A calorimetric study of several Bergerac-SH3 variants was carried out over a wide range of pH values and protein concentrations and the three-dimensional structure of one of them, SHH, was determined. X-ray studies confirmed that the nose had a well defined beta-structure whilst the chimera formed a stable tetramer within the crystal unit because of four tightly packed noses. In the pH range of 4-7 the heat-induced unfolding of some chimeras was complex and concentration dependent, whilst at pH values below 3.5, low protein concentrations of all the chimeras studied, including SHH, seemed to obey a monomolecular two-state unfolding model. The best set of data was obtained for the SHA variant, the unfolding heat effects of which were systematically higher than those of the WT protein (about 16.4 kJ/mol at 323 K), which may be close to the upper limit of the enthalpy gain due to 10 residue beta-hairpin folding. At the same time, the chimeras with high nose stability, which, like SHH, have a hydrophobic (IVY) cluster on their surface, showed a lower apparent unfolding heat effect, much closer to that of the WT protein. The possible reasons for this difference are discussed.

Prediction of structural stability of short beta-hairpin peptides by molecular dynamics and knowledge-based potentials

BACKGROUND

The structural stability of peptides in solution strongly affects their binding affinities and specificities. Thus, in peptide biotechnology, an increase in the structural stability is often desirable. The present work combines two orthogonal computational techniques, Molecular Dynamics and a knowledge-based potential, for the prediction of structural stability of short peptides (< 20 residues) in solution.

RESULTS

We tested the new approach on four families of short beta-hairpin peptides: TrpZip, MBH, bhpW and EPO, whose structural stabilities have been experimentally measured in previous studies. For all four families, both computational techniques show considerable correlation (r > 0.65) with the experimentally measured stabilities. The consensus of the two techniques shows higher correlation (r > 0.82).

CONCLUSION

Our results suggest a prediction scheme that can be used to estimate the relative structural stability within a peptide family. We discuss the applicability of this predictive approach for in-silico screening of combinatorial peptide libraries.

Heat-Capacity Changes in Host–Guest Complexation by Coulomb Interactions in Aqueous Solution

Heat-capacity changes (deltaC(p)0) were determined for the complexation of 1-alkanecarboxylates with protonated hexakis(6-amino-6-deoxy)-alpha-cyclodextrin (per-NH3(+)-alpha-CD) and heptakis(6-amino-6-deoxy)-beta-cyclodextrin (per-NH3(+)-beta-CD). DeltaC(p)0 decreased with an increase in the binding constant (K) and plateaued at K = 4000 M(-1). The complexes of 1-pentanoate, 1-hexanoate, and 1-heptanoate with per-NH3(+)-alpha-CD are classified as the host-guest system in which the size of the guest fits the CD cavity well. In such a system, van der Waals interaction is the major force for complexation, leading to a negative deltaH0 value. Simultaneously, the water molecules around the hydrophobic alkyl chain of the guest and inside the CD cavity are released to the aqueous bulk phase, leading to a positive deltaS0 value. The negative deltaC(p)0 value in such complexation is ascribed to dehydration of the hydrophobic alkyl chain of the guest and extrusion of the water molecules inside the CD cavity. Meanwhile, the complexes that show positive deltaC(p)0 values are characterized by complexation in which the guest molecules are significantly smaller than the CD cavities. In such a case, the complexation is endothermic and driven by the entropy gain. When the guest is much smaller than the CD cavity, the main binding force should be Coulomb interaction. To form an ionic bond, dehydration of the charged groups must occur. This process is endothermic and leads to positive deltaH0 and deltaS0 values. As the top of the CD cavity is capped by a small but hydrophobic alkyl chain, the water molecules inside the CD cavity may form the iceberg structure. This process must be accompanied by a positive deltaC(p)0 value. Hence, the complexation of a small guest with the CD with a large cavity through Coulomb interactions shows positive and large deltaC(p)0 values. These conclusions were applied to the electrostatic binding of proteins with an anionic ligand.

HEAT CAPACITY IN PROTEINS

Heat capacity (Cp) is one of several major thermodynamic quantities commonly measured in proteins. With more than half a dozen definitions, it is the hardest of these quantities to understand in physical terms, but the richest in insight. There are many ramifications of observed Cp changes: The sign distinguishes apolar from polar solvation. It imparts a temperature (T) dependence to entropy and enthalpy that may change their signs and which of them dominate. Protein unfolding usually has a positive deltaCp, producing a maximum in stability and sometimes cold denaturation. There are two heat capacity contributions, from hydration and protein-protein interactions; which dominates in folding and binding is an open question. Theoretical work to date has dealt mostly with the hydration term and can account, at least semiquantitatively, for the major Cp-related features: the positive and negative Cp of hydration for apolar and polar groups, respectively; the convergence of apolar group hydration entropy at T approximately 112 degrees C; the decrease in apolar hydration Cp with increasing T; and the T-maximum in protein stability and cold denaturation.

Thermodynamics of protein folding: a microscopic view

Statistical thermodynamics provides a powerful theoretical framework for analyzing, understanding and predicting the conformational properties of biomolecules. The central quantity is the potential of mean force or effective energy as a function of conformation, which consists of the intramolecular energy and the solvation free energy. The intramolecular energy can be reasonably described by molecular mechanics-type functions. While the solvation free energy is more difficult to model, useful results can be obtained with simple approximations. Such functions have been used to estimate the intramolecular energy contribution to protein stability and obtain insights into the origin of thermodynamic functions of protein folding, such as the heat capacity. With reasonable decompositions of the various energy terms, one can obtain meaningful values for the contribution of one type of interaction or one chemical group to stability. Future developments will allow the thermodynamic characterization of ever more complex biological processes.

The thermodynamics of protein-protein recognition as characterized by a combination of volumetric and calorimetric techniques: the binding of turkey ovomucoid third domain to alpha-chymotrypsin

We have used ultrasonic velocimetry, high-precision densimetry, and fluorescence spectroscopy, in conjunction with isothermal titration and differential scanning calorimetry, to characterize the binding of turkey ovomucoid third domain (OMTKY3) to alpha-chymotrypsin. We report the changes in volume and adiabatic compressibility that accompany the association of these proteins at 25 degrees C and pH 4.5. In addition, we report the changes in free energy, enthalpy, entropy, and heat capacity upon the binding of OMTKY3 to alpha-chymotrypsin over a temperature range of 20-40 degrees C. Our volume and compressibility data, in conjunction with X-ray crytsallographic data on the OMTKY3-alpha-chymotrypsin complex, suggest that 454(+/-22) water molecules are released to the bulk state upon the binding of OMTKY3 to alpha-chymotrypsin. Furthermore, these volumetric data suggest that the intrinsic compressibility of the two proteins decreases by 7%. At each temperature studied, OMTKY3 association with alpha-chymotrypsin is entropy driven with a large, unfavorable enthalpy contribution. The observed entropy of the binding reflects interplay between two very large favorable and unfavorable terms. The favorable term reflects an increase in the hydrational entropy resulting from release to the bulk of 454 water molecules. The unfavorable term is related to a decrease in the configurational entropy and, consequently, a decrease in the conformational dynamics of the two proteins. In general, we discuss the relationship between macroscopic and microscopic properties, in particular, identifying and quantifying the role of hydration in determining the thermodynamics of protein recognition as reflected in volumetric and calorimetric parameters.

Anti-cooperativity and cooperativity in hydrophobic interactions: Three-body free energy landscapes and comparison with implicit-solvent potential functions for proteins

Potentials of mean force (PMFs) of three-body hydrophobic association are investigated to gain insight into similar processes in protein folding. Free energy landscapes obtained from explicit simulations of three methanes in water are compared with that predicted by popular implicit-solvent effective potentials for the study of proteins. Explicit-water simulations show that for an extended range of three-methane configurations, hydrophobic association at 25 degrees C under atmospheric pressure is mostly anti-cooperative, that is, less favorable than if the interaction free energies were pairwise additive. Effects of free energy nonadditivity on the kinetic path of association and the temperature dependence of additivity are explored by using a three-methane system and simplified chain models. The prevalence of anti-cooperativity under ambient conditions suggests that driving forces other than hydrophobicity also play critical roles in protein thermodynamic cooperativity. We evaluate the effectiveness of several implicit-solvent potentials in mimicking explicit water simulated three-body PMFs. The favorability of the contact free energy minimum is found to be drastically overestimated by solvent accessible surface area (SASA). Both the SASA and a volume-based Gaussian solvent exclusion model fail to predict the desolvation barrier. However, this barrier is qualitatively captured by the molecular surface area model and a recent "hydrophobic force field." None of the implicit-solvent models tested are accurate for the entire range of three-methane configurations and several other thermodynamic signatures considered.

Contributions to the binding free energy of ligands to avidin and streptavidin

The free energy of binding of a ligand to a macromolecule is here formally decomposed into the (effective) energy of interaction, reorganization energy of the ligand and the macromolecule, conformational entropy change of the ligand and the macromolecule, and translational and rotational entropy loss of the ligand. Molecular dynamics simulations with implicit solvation are used to evaluate these contributions in the binding of biotin, biotin analogs, and two peptides to avidin and streptavidin. We find that the largest contribution opposing binding is the protein reorganization energy, which is calculated to be from 10 to 30 kcal/mol for the ligands considered here. The ligand reorganization energy is also significant for flexible ligands. The translational/rotational entropy is 4.5-6 kcal/mol at 1 M standard state and room temperature. The calculated binding free energies are in the correct range, but the large statistical uncertainty in the protein reorganization energy precludes precise predictions. For some complexes, the simulations show multiple binding modes, different from the one observed in the crystal structure. This finding is probably due to deficiencies in the force field but may also reflect considerable ligand flexibility.

Polymer principles of protein calorimetric two-state cooperativity

The experimental calorimetric two-state criterion requires the van't Hoff enthalpy DeltaH(vH) around the folding/unfolding transition midpoint to be equal or very close to the calorimetric enthalpy DeltaH(cal) of the entire transition. We use an analytical model with experimental parameters from chymotrypsin inhibitor 2 to elucidate the relationship among several different van't Hoff enthalpies used in calorimetric analyses. Under reasonable assumptions, the implications of these DeltaH(vH)'s being approximately equal to DeltaH(cal) are equivalent: Enthalpic variations among denatured conformations in real proteins are much narrower than some previous lattice-model estimates, suggesting that the energy landscape theory "folding to glass transition temperature ratio" T(f) /T(g) may exceed 6.0 for real calorimetrically two-state proteins. Several popular three-dimensional lattice protein models, with different numbers of residue types in their alphabets, are found to fall short of the high experimental standard for being calorimetrically two-state. Some models postulate a multiple-conformation native state with substantial pre-denaturational energetic fluctuations well below the unfolding transition temperature, or predict a significant post-denaturational continuous conformational expansion of the denatured ensemble at temperatures well above the transition point, or both. These scenarios either disagree with experiments on protein size and dynamics, or are inconsistent with conventional interpretation of calorimetric data. However, when empirical linear baseline subtractions are employed, the resulting DeltaH(vH)/DeltaH(cal)'s for some models can be increased to values closer to unity, and baseline subtractions are found to correspond roughly to an operational definition of native-state conformational diversity. These results necessitate a re-assessment of theoretical models and experimental interpretations.

Modeling protein density of states: additive hydrophobic effects are insufficient for calorimetric two-state cooperativity

A well-established experimental criterion for two-state thermodynamic cooperativity in protein folding is that the van't Hoff enthalpy DeltaH(vH) around the transition midpoint is equal, or very nearly so, to the calorimetric enthalpy DeltaH(cal) of the entire transition. This condition is satisfied by many small proteins. We use simple lattice models to provide a statistical mechanical framework to elucidate how this calorimetric two-state picture may be reconciled with the hierarchical multistate scenario emerging from recent hydrogen exchange experiments. We investigate the feasibility of using inverse Laplace transforms to recover the underlying density of states (i.e., enthalpy distribution) from calorimetric data. We find that the constraint imposed by DeltaH(vH)/DeltaH(cal) approximately 1 on densities of states of proteins is often more stringent than other "two-state" criteria proposed in recent theoretical studies. In conjunction with reasonable assumptions, the calorimetric two-state condition implies a narrow distribution of denatured-state enthalpies relative to the overall enthalpy difference between the native and the denatured conformations. This requirement does not always correlate with simple definitions of "sharpness" of a transition and has important ramifications for theoretical modeling. We find that protein models that assume capillarity cooperativity can exhibit overall calorimetric two-state-like behaviors. However, common heteropolymer models based on additive hydrophobic-like interactions, including highly specific two-dimensional Gō models, fail to produce proteinlike DeltaH(vH)/DeltaH(cal) approximately 1. A simple model is constructed to illustrate a proposed scenario in which physically plausible local and nonlocal cooperative terms, which mimic helical cooperativity and environment-dependent hydrogen bonding strength, can lead to thermodynamic behaviors closer to experiment. Our results suggest that proteinlike thermodynamic cooperativity may require a cooperative interplay between local and nonlocal interactions. The prospect of using calorimetric data to constrain Z-scores of knowledge-based potentials is discussed.

Is protein unfolding the reverse of protein folding? A lattice simulation analysis

Simulations and experiments that monitor protein unfolding under denaturing conditions are commonly employed to study the mechanism by which a protein folds to its native state in a physiological environment. Due to the differences in conditions and the complexity of the reaction, unfolding is not necessarily the reverse of folding. To assess the relevance of temperature initiated unfolding studies to the folding problem, we compare the folding and unfolding of a 125-residue protein model by Monte Carlo dynamics at two temperatures; the lower one corresponds to the range used in T -jump experiments and the higher one to the range used in unfolding simulations of all-atom models. The trajectories that lead from the native state to the denatured state at these elevated temperatures are less diverse than those observed in the folding simulations. At the lower temperature, the system unfolds through a mandatory intermediate that corresponds to a local free energy minimum. At the higher temperature, no such intermediate is observed, but a similar pathway is followed. The structures contributing to the unfolding pathways resemble most closely those that make up the "fast track" of folding. The transition state for unfolding at the lower temperature (above Tm) is determined and is found to be more structured than the transition state for folding below the melting temperature. This shift towards the native state is consistent with the Hammond postulate. The implications for unfolding simulations of higher resolution models and for unfolding experiments of proteins are discussed.